Should Mississippians hunt deer or rabbits? What game theory can tell us about brain drain

Mississippi is stuck in a bad equilibrium that gives its educated young people little incentive to stay.

This is the first of a two-part series analyzing the economics behind Mississippi’s brain drain. Part two delves into economic research for ideas to reverse Mississippi’s net outmigration rate.

Jake McGraw has written on this site about what he calls Mississippi’s greatest challenge: retaining and attracting people who have the ability to live elsewhere. Between 2000 and 2010, more people moved away from Mississippi than moved in. Aside from Louisiana’s post-Katrina exodus, Mississippi’s net outmigration rate was alone among the Southern states during that period, and recent data show the problem has continued.

When an area loses more residents than it gains, it can expect fewer new businesses to open and more existing ones to close their doors. Property values and investment will decline. Political representation in state and national government will be ceded to faster-growing areas. These factors lead to lower levels of employment and income for the people who remain, and subsequently even more dismal growth prospects.

Although the potential problems are clear, it is difficult to see an obvious way out of this trap. In this series, I will look at the basic “stay or go?” choice presented to many young Mississippians. In a way, this is a very personal issue for me, as I and many of my friends have pursued opportunities out of state that simply weren’t available to us in Mississippi. The state’s future may depend on a solid understanding of why people choose to leave and what can be done to avoid the vicious cycle of decline that often accompanies outmigration.

The “Stag Hunt” game

Solving the riddle of brain drain may require new ways of thinking about the problem. I propose we examine outmigration through one of our state’s favorite pastimes: hunting.

Take the example of two hunters, Bobby and Hank, who head into the woods looking for either deer or rabbit. It will take both of them to kill, dress, and cook a deer, but only one to kill and prepare a rabbit. The deer will provide 100 pounds of meat, to be split between the two. They can each hunt multiple rabbits, but a haul of 10 apiece would yield at most 30 pounds of meat.

Bobby and Hank each must decide for himself which animal he will hunt. Here’s the important part: they cannot speak to one another before they make their decisions.

Both hunters know that the potential payoff is greater by choosing to hunt deer, but so is the risk. Before Bobby decides to hunt deer, he must be confident that Hank will also choose to hunt deer. If Bobby hunts deer while Hank hunts rabbits, Bobby will go home empty-handed. The safer choice would be to hunt rabbit separately, even though that means settling for less meat than they would have gained cooperatively.

The problem is illustrated in this payoff matrix:

The grid above maps each hunters’ choices to their payoffs. In each cell, the number to the left is the pounds of meat Hank gets, while the number to the right is the number of pounds Bobby gets. The “good” equilibrium is highlighted in green, the “bad” in red.

This is a classic game theory problem known as the Stag Hunt. The game has two equilibria — stable outcomes in which no participant has an incentive to deviate from his or her course of action given the decision of the other. The game is in equilibrium only when the hunters choose to do the same thing: either both hunters go off on their own to hunt rabbit or they both go after the deer. If they chose to hunt different animals, the deer hunter would soon realize he’s going to starve and change his decision, thus resetting to equilibrium.

One equilibrium is clearly superior to the other. Each hunter maximizes the amount of meat in his freezer when they both choose to hunt deer. If both choose to hunt rabbits, they will each get to eat, albeit 20 pounds less than if they’d both hunted deer.

Both would benefit from cooperation, but without the ability to communicate, Bobby and Hank must try to guess what the other is thinking. They will be more likely to hunt rabbits separately — accepting a lower payoff in exchange for less risk if they guess wrong.

To stay or to go?

Mississippi faces a similar collective action problem. Many young Mississippians must choose whether to stay in the state or move elsewhere, but they cannot coordinate their decisions with the thousands of others facing a similar conundrum.

We can model this scenario in the same way we did with the hunting story above by imagining, for simplicity, that there are only two people with college degrees in Mississippi, Peggy and Luanne. They’re recent graduates, and they have to decide whether to stay in the state or move to a city in a neighboring state where there are many college graduates. [1]

Let’s assume that living in the same place as other college graduates gives these recent graduates a higher income. There are many reasons why this would be true in reality. For instance, the presence of skilled workers may be indicative of a higher concentration of entrepreneurs, resulting in wider career opportunities in an area. Working with other college graduates may also improve a person’s productivity and earnings potential in any particular job. (We’ll examine some real data on this phenomenon in the second part of this series.)

It is helpful to illustrate with specific figures. If both Luanne and Peggy decide to stay in Mississippi, they will each earn $41,000 a year. But by moving to a neighboring state with a higher concentration of skilled workers, each grad could earn $45,000 regardless of the other’s decision.[2] However, if Luanne leaves and Peggy decides to stay in Mississippi, Peggy would earn considerably less, say $28,000, without another skilled worker around.

Of course, not all places are made the same. Let’s say that both Peggy and Luanne would prefer to stay in Mississippi if they could. They like being near their family and friends, they like going to their favorite restaurants and bars, and they love going to every Ole Miss home game. If you suppose that they value all of these things equivalent to $10,000 per year, the payoff matrix looks like this:

As above, the number to the left is Peggy’s payoff to each action pairing, and the number to the right is Luanne’s. The units are thousands of dollars. Note that the payoffs to (Stay Home, Stay Home) include the salary of college grads in Mississippi ($41,000) plus the extra benefit of being at home ($10,000). These numbers are based on real income data for college graduates in Mississippi and Alabama.

Just as in the hunting problem, there are two equilibria: a good one in which both college grads stay in Mississippi and have higher payoffs, and a bad one in which both move to the neighboring state and have lower payoffs. If one chooses to leave while the other stays, then the expected salary in Mississippi would drop so much that the grad who stayed would have even greater incentive to change her decision and leave — thus settling on the bad equilibrium.

We can extend this model to a scenario in which there are many skilled workers facing the same sort of stay-or-go decision. The principle remains the same: the benefit of staying depends on how many others decide to stay in the state. A critical mass of skilled workers creates a more productive economy, thereby increasing incomes to a level competitive with surrounding areas. A good equilibrium can become self-sustaining, such as in Nashville, Raleigh, Atlanta, and other places that have become magnets for young, skilled migrants.

Mississippi’s bad equilibrium

To this point, the ideas of good and bad equilibria may just sound like theoretical constructions. In Mississippi, their effects are very real.

The experience of the Delta typifies the downward economic spiral that can occur when an area is stuck in a bad equilibrium. It is also a prime example of the types of things that can get an area started moving in the right or wrong direction.[3]

During the first half of the last century, the promise of a respectable living farming brought people to the Delta. The area was in a good equilibrium of self-sustaining growth: as agriculture attracted flocks of laborers, even more came to open restaurants and dry cleaners and other businesses whose profitability depended only on the fact that there were other people there already.

By the 1940s, however, technological progress and globalization had begun to bring about the Delta’s decline. The work previously done by Mississippians was increasingly performed by machines or by cheaper labor in developing countries. The Delta’s population peaked in 1940 at about 430,000. Since then it has dropped rapidly. As of 2012, only 217,500 people lived in the Delta, almost exactly half as many as 70 years prior.

Not surprisingly, the population decline has mirrored the erosion of agricultural jobs. The number of people working on farms in the Delta in 1954, the earliest year for which comprehensive employment data are available, was 145,000, roughly 35% of the total population. In 2007, the most recent year with data available, farm labor in the Delta had declined to only 7,000, or about 3% of the total population.

People started leaving the Delta when employment in farming waned, but employment in ancillary industries soon followed. The Delta’s declining labor force triggered a shrinking tax base and increasing concentration of poverty. These factors, along with the legacy of a long and troubled social history, have contributed to the poor performance of the Delta’s school districts — further inducing those with the ability to leave to do so.

In the second part of this series, I will examine some of the research into how areas like the Delta (and Mississippi more generally) can escape their bad equilibria. The best long-term policy prescription is education. Although improving education is by no means a novel solution, recent economic research can be used to make predictions as to how this apparent cure-all can help lead an area out of the outmigration trap.

[1] Although I frame the discussion in terms of college graduates’ dilemma, they are not the only group relevant to this problem — the argument applies to any type of skilled workers or entrepreneurs.[2] These data reflect actual average salaries for college graduates in Mississippi and Alabama.

In this article

A native of Oxford, Neil White is a graduate student in economics at the University of Texas at Austin. Neil previously worked for the Bureau of Labor Statistics in Washington, D.C. He holds a bachelor's degree in economics from Princeton University. You can contact him at neil.whiteiv@gmail.com.